To look for candidate metabolite-methylation pairs, I ran three linear models and selected based on the p value cutoffs below (e.g. metabolite and methylation associated at p < 0.05, and both associated with IA status at p < 0.05).
Using this mediation structure, there were 516 pairs selected. The only metabolite selected was lipid_582:
| identifier | row.m.z | row.retention.time | Metabolite.name | InChi.Key | mode | bc.lambda | feature_name | |
|---|---|---|---|---|---|---|---|---|
| 582 | 1.39_301.22 | 301.2157 | 1.39 | FA (20:5) [M-H]- (eicosapentaenoic acid)_JAZBEHYOTPTENJ-JLNKQSITSA-N | JAZBEHYOTPTENJ-JLNKQSITSA-N | negative | -0.6 | lipid_582 |
No pairs were selected using this mediation structure.
Terms:
\[ Y = \text{IA Status}\\ M = \text{Metabolite at SV}\\ T = \text{Methylation at PSV}\\ X_2 = \text{Age at PSV}\\ X_3 = \text{Sex}\\ X_4 = \text{DR3/4 Status}\\ \text{i indexes subject}\\ \]
\[ M_i = \beta_0 + \beta_1 T_i+\beta_2 X_{i2}+\beta_3 X_{i3}+\beta_4 X_{i4}+\epsilon_i\\ \text{With } \epsilon_i\text{ i.i.d. } N(0,\sigma^2) \]
\[ \text{Let }p=\text{the probability a given subject is an IA case}=P(Y = 1)\\ ln(\frac{p}{1-p}) = \theta_0 +\theta_1 T_i+\theta_2 M_i+\theta_3 X_{i2}+\theta_4 X_{i3}+\theta_5 X_{i4} \]
Given, the observed outcome \(Y_i(T_i, M_i(T_i))\), where \(M_i(T_i)\) represents the observed value of the mediator:
\[ \text{CME: }\delta_i(t)\equiv Y_i(t, M_i(1)) − Y_i(t, M_i(0))\\ \text{DE: } \gamma_i(t)\equiv Y_i(1, M_i(t)) − Y_i(0, M_i(t))\\ \text{TE: } \tau_i\equiv \delta_i(t)+\gamma_i(1−t) \]
mediation package| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | -0.0452892 | 0.0229637 | -1.972212 | 0.054615 |
| manual | 0.5341016 | 0.0659520 | 8.098341 | 0.000000 |
The slope of this linear model is significantly different from 1 (p < 0.001). However, a t test of the difference is not statistically significant (p = 0.711). All of the signs are the same at least.
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | -0.4680276 | 0.1106164 | -4.231085 | 0.0001097 |
| manual | 0.4271809 | 0.0562433 | 7.595230 | 0.0000000 |
The slope of this linear model is significantly different from 1 (p < 0.001). However, a t test of the difference is not statistically significant (p = 0.12). The signs are not all the same, but the one that is different is very close (-0.00323 vs. 0.00209).
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 0.0036778 | 0.0222009 | 0.1656617 | 0.8691491 |
| manual | 0.9369964 | 0.0454057 | 20.6361161 | 0.0000000 |
The slope of this linear model is significantly different from 1 (p < 0.001). However, a t test of the difference is not statistically significant (p = 0.233). All signs are the same.
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | -0.0010031 | 0.0162974 | -0.0615482 | 0.9511893 |
| manual | -0.0419505 | 0.0488918 | -0.8580268 | 0.3953264 |
The slope of this linear model is significantly different from 1 (p < 0.001). However, a t test of the difference is not statistically significant (p = 0.919). The signs are pretty different.
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | -0.1072940 | 0.0175911 | -6.099337 | 0.0000002 |
| manual | -0.0762647 | 0.0264451 | -2.883889 | 0.0059567 |
The slope of this linear model is significantly different from 1 (p < 0.001). Also, a t test of the difference was statistically significant (p = <0.001). The signs are not all the same.
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 0.1104663 | 0.0276074 | 4.001322 | 0.0002269 |
| manual | -0.0846191 | 0.0490265 | -1.725987 | 0.0910619 |
The slope of this linear model is significantly different from 1 (p < 0.001). A t test of the difference was also statistically significant (p = <0.001).
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 0.0018581 | 0.0027858 | 0.6670026 | 0.5081026 |
| manual | -0.0016904 | 0.0014292 | -1.1827167 | 0.2429986 |
The slope of this linear model is significantly different from 1 (p < 0.001). However, a t test of the difference is not statistically significant (p = 0.871). The signs are pretty different.
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | -0.0598664 | 0.0087648 | -6.830361 | 0.000000 |
| manual | -0.0139536 | 0.0034697 | -4.021530 | 0.000213 |
The slope of this linear model is significantly different from 1 (p < 0.001). Also, a t test of the difference was statistically significant (p = <0.001). The signs are not all the same.
What is happening here?
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 0.0602508 | 0.0075195 | 8.01258 | 0.0000000 |
| manual | -0.0096862 | 0.0026415 | -3.66687 | 0.0006349 |
The slope of this linear model is significantly different from 1 (p < 0.001). A t test of the difference was also statistically significant (p = <0.001).
regmedint package## Warning in summary.lm(lm(package ~ manual)): essentially perfect fit: summary
## may be unreliable
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 0 | 0 | -3.047864e+00 | 0.0038121 |
| manual | 1 | 0 | 3.311232e+16 | 0.0000000 |
The package and my code match perfectly.
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 0.0435322 | 0.0317348 | 1.37175 | 0.1767951 |
| manual | 0.4472601 | 0.0161357 | 27.71875 | 0.0000000 |
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 0.1947107 | 0.0378399 | 5.145644 | 0.0000054 |
| manual | 0.2061689 | 0.0773908 | 2.663997 | 0.0106103 |
## Warning in summary.lm(lm(package ~ manual)): essentially perfect fit: summary
## may be unreliable
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 0 | 0 | 0.000000e+00 | 1 |
| manual | 1 | 0 | 1.294429e+17 | 0 |
They match perfectly again!
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | -0.0472334 | 0.0053649 | -8.804103 | 0 |
| manual | 0.8154650 | 0.0080652 | 101.108850 | 0 |
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 0.0759720 | 0.0087218 | 8.710571 | 0 |
| manual | 0.7234295 | 0.0154886 | 46.707291 | 0 |
The slope of this linear model is significantly different from 1 (p < 0.001). A t test of the difference was also statistically significant (p = 0.0417).
## Warning in summary.lm(lm(package ~ manual)): essentially perfect fit: summary
## may be unreliable
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 0 | 0 | -2.602018e-01 | 0.7958693 |
| manual | 1 | 0 | 1.582513e+16 | 0.0000000 |
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 0.0010130 | 0.0154580 | 0.0655309 | 0.9480353 |
| manual | 0.9113554 | 0.0061194 | 148.9280735 | 0.0000000 |
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 0.0004431 | 0.0186194 | 0.0237978 | 0.9811168 |
| manual | 0.9192607 | 0.0065408 | 140.5416437 | 0.0000000 |